Question

/*
 * ezThreeFourths - multiplies by 3/4 rounding toward 0,
 *   Should exactly duplicate effect of C expression (x*3/4),
 *   including overflow behavior.
 *   Examples: ezThreeFourths(11) = 8
 *             ezThreeFourths(-9) = -6
 *             ezThreeFourths(1073741824) = -268435456 (overflow)
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 3
 */

int ezThreeFourths(int x) {
   int z = x+x+x;
   int sign_z = z>>31;
   return ((z>>2)&(~sign_z)) + (((z>>2)+1)&sign_z);
}

我试图解决这个难题，但


ERROR: Test ezThreeFourths(-2147483648[0x80000000]) failed...
...Gives -536870911[0xe0000001]. Should be -536870912[0xe0000000]

使用gcc（GCC）4.1.2 20080704（Red Hat 4.1.2-51）编译

这个解决方案有什么问题？

Answer 1

这就是我的所作所为：

#include <stdio.h>
#include <limits.h>

int ThreeFourths(int x)
{
  int x3 = x + x + x;
  return (x3 >= 0) ? (x3 >> 2) : -(int)((UINT_MAX - x3 + 1) >> 2);
}

int testData[] =
{
   0,
   1,
  -1,
   2,
  -2,
   3,
  -3,
   4,
  -4,
   5,
  -5,
  -9,
  11,
  INT_MAX / 2 + 1,
  INT_MIN
};

int main(void)
{
  int i;

  for (i = 0; i < sizeof(testData)/sizeof(testData[0]); i++)
  {
    printf("      %d * 3 / 4 = %d\n",
           testData[i], testData[i] * 3 / 4);
    printf("ThreeFourths(%d) = %d\n",
           testData[i], ThreeFourths(testData[i]));
  }
  return 0;
}

输出：

      0 * 3 / 4 = 0
ThreeFourths(0) = 0
      1 * 3 / 4 = 0
ThreeFourths(1) = 0
      -1 * 3 / 4 = 0
ThreeFourths(-1) = 0
      2 * 3 / 4 = 1
ThreeFourths(2) = 1
      -2 * 3 / 4 = -1
ThreeFourths(-2) = -1
      3 * 3 / 4 = 2
ThreeFourths(3) = 2
      -3 * 3 / 4 = -2
ThreeFourths(-3) = -2
      4 * 3 / 4 = 3
ThreeFourths(4) = 3
      -4 * 3 / 4 = -3
ThreeFourths(-4) = -3
      5 * 3 / 4 = 3
ThreeFourths(5) = 3
      -5 * 3 / 4 = -3
ThreeFourths(-5) = -3
      -9 * 3 / 4 = -6
ThreeFourths(-9) = -6
      11 * 3 / 4 = 8
ThreeFourths(11) = 8
      1073741824 * 3 / 4 = -268435456
ThreeFourths(1073741824) = -268435456
      -2147483648 * 3 / 4 = -536870912
ThreeFourths(-2147483648) = -536870912

我没有在负整数上使用右移的原因很简单。这些转换的结果是实现定义的（根据C标准），并且不保证与我们可能期望的符号扩展的右移相同，因为它是最常见的实现。

我写了(UINT_MAX - x3 + 1)而不仅仅是-x3，因为它可能导致签名溢出（当x3 = INT_MIN为2的负幂时），这是未定义的行为（再次按照C标准）。即使已知这种未定义的行为是无害的，简单的否定仍然无法产生正数（因为有符号整数的2的补码表示中的不对称性）。

x + x + x仍然可以像x * 3一样产生签名溢出。所以，这是相同的未定义行为。

顺便说一下，由于签名溢出导致UB，甚至不应该从法律上要求你实现它们，更不用说对UB发生时的结果有特定的期望。

Answer 2

int ezThreeFourths(int x) {  


  int z = x+x+x;  
  int sign_z = z>>31;  


  return ((z>>2)&(~sign_z)) + (((z>>2)+1)&sign_z);  

}

使用非负数。你也不应该对code "you" wrote撒谎。考虑到确切的代码写在“2008-01-26”

Answer 3

使用Embarcadero C ++ 6.43为我工作正常：

// x = 2147483647
int ezThreeFourths(int x)
{
    int z = x+x+x;
    // z = 2147483645 (6442450941[0x17FFFFFFD] truncated to 32-bits!)

    int sign_z = z>>31;
    // sign_z = (2147483645 >> 31) = 0

    return ((z>>2)&(~sign_z)) + (((z>>2)+1)&sign_z);
    // = ((2147483645 >> 2) & (~0)) + (((2147483645 >> 2) + 1) & 0)
    // = (536870911 & 0xFFFFFFFF) + ((536870911+1) & 0)
    // = (536870911 & 0xFFFFFFFF) + (536870912 & 0)
    // = (536870911 & 0xFFFFFFFF) + 0
    // = (536870911 & 0xFFFFFFFF)
    // = 536870911
}

Answer 4

在输入值均匀分为4的情况下，将负数舍入为零的方法无法正常工作.0x80000000就是这样一个示例，但如果尝试使用较小的值，则可能更容易看到问题。

例如：ezThreeFourths（-8）= -5 [应为-6]

C位操作难题

4 个答案: